The multiple Dirichlet product and the multiple Dirichlet series

PreprintEnglishOPEN

Onozuka, Tomokazu;

(2016)

Subject: 11M32, 11A25 | Mathematics - Number Theory

arxiv: Mathematics::Spectral Theory | Mathematics::Analysis of PDEs

First, we define the multiple Dirichlet product and study the properties of it. From those properties, we obtain a zero-free region of a multiple Dirichlet series and a multiple Dirichlet series expression of the reciprocal of a multiple Dirichlet series.